Bayesian functional linear regression with sparse step functions

Paul-Marie Grollemund (1, 2) , Christophe Abraham (2) , Meïli Baragatti (2) , Pierre Pudlo (3)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie
3 I2M - Institut de Mathématiques de Marseille

The functional linear regression model is a common tool to determine the relationship between a scalar outcome and a functional predictor. This paper focuses on the interpretability of the estimation of the coefficient function of this model. We propose a Bayesian functional Linear regression with Sparse Step functions (Bliss). The aim of the method is to provide interpretable estimates: the Bayesian model is based on an adaptive decomposition of the coefficient function into sparse and simple functions. A Bayes estimator is constructed with a specific loss function. The method is compared to its competitors on simulated datasets and is illustrated on a black Périgord truffle dataset.

Mots clés: Bayesian regression; function data; interpretability; parsimony

Domaines: Méthodologie [stat.ME]; Statistiques [math.ST]

Paul-Marie Grollemund, Christophe Abraham, Meïli Baragatti, Pierre Pudlo. Bayesian functional linear regression with sparse step functions. 2016. ⟨hal-01308830v1⟩